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Investigation of a post-tensioned timber connectiontest report

Author(s): Frangi, Andrea; Wanninger, Flavio

Publication Date: 2014

Permanent Link: https://doi.org/10.3929/ethz-a-010232009

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i b kInstitut für Baustatik und Konstruktion, ETH Zürich

Investigation of a post-tensioned timber connection

Flavio WanningerAndrea Frangi

IBK Bericht Nr. 355, Juni 2014

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KEYWORDS: Timber, hardwood, connection, post-tensioned, static tests, embedment failure

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Flavio Wanninger, Andrea Frangi: Investigation of a post-tensioned timber connection

Bericht IBK Nr. 355, Juni 2014

© 2014 Institut für Baustatik und Konstruktion der ETH Zürich, Zürich

Gedruckt auf säurefreiem PapierPrinted in Switzerland

Investigation of a post-tensioned timber connection

Test report

Flavio Wanninger

Andrea Frangi

Institute of Structural Engineering

Swiss Federal Institute of Technology Zurich

Zurich

August 2014

i

Foreword

In the past decades, precast concrete frames were developed using tendons to connect columns

and beams. These systems showed favourable seismic behaviour, being able to avoid residual

deformations after an earthquake. The use of post-tensioned timber structures was recently

studied at the Institute of Structural Engineering at the ETH in Zurich in the framework of

the Master Thesis of Roman Schneider in cooperation with the industrial partner Haring & Co.

AG. As a result, an innovative post-tensioned beam-column timber joint was developed using

glued laminated timber made of spruce and local strengthening of the joint with hardwood.

The present report shows the results of a comprehensive series of static bending tests on the

developed post-tensioned beam-column timber joint. The experimental investigations were con-

ducted in the framework of the research project entitled ”Post-tensioned timber frame struc-

tures” and sponsored by the Commission of Technology and Innovation CTI and supported by

the industrial partner Haring & Co. AG, Eiken. The overall objective of the research project

is the development and implementation of post-tensioned timber frame structures. The project

fits into the overall research strategy of the institute on the development of innovative solutions

for timber structures. The tests presented in this report form one important step to evaluate

the moment-rotation-behaviour of the developed post-tensioned beam-column timber joint. The

test results demonstrate the high stiffness of the joint and the nonlinear structural behaviour

after the moment of decompression. Furthermore, even after large rotations, the timber column

showed only small residual deformations due to compression perpendicular to the grain.

I would like to thank Flavio Wanninger who has prepared and carefully conducted all tests

and has also processed and evaluated the large amount of data and edited this report. I would

also like to thank the team of the IBK testing and research lab (Patrik Morf, Christoph Gisler,

Thomas Jaggi, Pius Herzog and Dominik Werne) and Christian Nagy as well as Claudio Scan-

della for their support. Furthermore, I would like to gratefully acknowledge the support by the

Swiss Commission for Technology and Innovation (CTI) and the industrial partner Haring &

Co. AG.

Zurich, June 2014 Andrea Frangi

iii

Summary

A post tensioned timber connection made of glulam has been developed at the ETH in Zurich.

The connection is made of spruce with ash reinforcement in the connection area where high

stresses perpendicular to the grain occur.

The moment-rotation-behaviour of this post-tensioned beam-column timber joint has been anal-

ysed with a series of static bending tests. The timber joint was loaded at the ends of the beams

in order to apply a moment to the connection. The tests were conducted with different forces

in the tendon, from 300 kN up to 700 kN. The bending tests were performed with a controlled

load level, so that no embedment failure perpendicular to the grain occurred in the column. The

intended self-centring behaviour could be verified and no damage could be observed during all

the tests.

A final bending test was conducted in order to study the failure mode of the post-tensioned tim-

ber connection. The vertical load on the beams was increased until the tendon-elongation got so

high that the test had to be aborted due to safety reasons. Nearly no damage occurred during

the last test, only minor residual deformations could be observed. The failure is an embedment

failure in the column due to exceedance of the strength perpendicular to the grain.

The specimen, test setup, instrumentation and the results of all performed tests are presented

in this technical report.

Keywords: Timber, hardwood, connection, post-tensioned, static tests, embedment failure

v

Zusammenfassung

Einfache und wirtschaftliche biegesteife Verbindungen sind im Holzbau schwierig zu realisieren.

Am Institut fur Baustatik und Konstruktion der ETH Zurich wurde in Zusammenarbeit mit der

Firma Haring & Co. AG der Prototyp einer neuartigen vorgespannten Holzrahmenkonstruktion

entwickelt.

Der Trager-Stutze-Knotenanschluss aus Brettschichtholz mit lokaler Verstarkung aus Hartholz

uberzeugt durch den hohen Vorfertigungsgrad und dem zeitsparendem Zusammenfugen auf der

Baustelle dank des einfachen Aufbaus des Systems. Er zeigt das grosse Potential von vorges-

pannten Holzrahmenkonstruktionen insbesondere fur mehrgeschossige Holzbauten.

Der Prototyp wurde in einer Serie von Biegeversuchen auf sein Tragverhalten untersucht. Samtliche

Versuche wurden mit unterschiedlichen Vorspannkraften gefahren. Die Vorspannkraft variierte

- je nach Versuch - zwischen 300 kN und 700 kN. Die Versuche wurden mit einer Belastung

durchgefuhrt, welche zu keinen Schaden am Versuchskorper fuhrten. Neben einer symmetrischen

Belastung des Knotens wurden auch asymmetrisch Lastfalle gefahren, welche eine horizontale

Belastung des Knotens simulieren sollten (Windlasten, Erdbeben). Das selbst-zentrierende Ver-

halten des Knotens konnte bestatigt werden, ohne dass der Knoten beschadigt wurde.

In einem letzten Biegeversuch sollten die Lasten gesteigert werden, bis ein Versagen des Systems

eintritt. Durch die hohen Deformationen am Knoten wurde das Spannglied verlangert, was zu

einer Zunahme der Vorspannkraft fuhrte. Diese Zunahme wurde so gross, dass der Versuch

aus Sicherheitsgrunden abgebrochen wurde. Der Schaden am Knoten war sehr gering, lediglich

kleine bleibende Verformungen infolge Querdruck senkrecht zur Faserung in der Stutze waren

die Folge.

Dieser Versuchsbericht beinhaltet samtliche Informationen zum Versuchsaufbau und -korper,

sowie Versuchsbeschrieb und -auswertung aller durchgefuhrten Versuche.

Contents

1 Introduction 1

2 Specimen and test setup 3

2.1 Material and dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Test setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.3 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3.1 Linear variable differential transformers . . . . . . . . . . . . . . . . . . . 6

2.3.2 Inclinometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3.3 Pressure sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3.4 Hydraulic pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3.5 Load cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3 Test overview 11

3.1 Testing program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.1.1 Test protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.2 Testing procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4 Experimental analysis - equations 15

4.1 Initial compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.2 Key variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.2.1 LVDTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.2.2 Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4.2.3 Moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.2.4 Decompression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.2.5 Neutral axis depth from LVDTs . . . . . . . . . . . . . . . . . . . . . . . 21

4.2.6 Stresses in the column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

5 Experimental analyis - test evaluation 23

5.1 Test 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

5.1.1 Initial compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

viii CONTENTS

5.1.2 Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

5.1.3 Evaluation symmetrical loading . . . . . . . . . . . . . . . . . . . . . . . . 25

5.1.4 Evaluation asymmetrical loading - constant load on right beam . . . . . . 27

5.1.5 Evaluation asymmetrical loading - constant load on left beam . . . . . . . 28

5.2 Test 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29


5.2.2 Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29


5.2.4 Evaluation symmetrical loading - constant load on right beam . . . . . . 31


5.3 Test 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33


5.3.2 Rotation test 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34




5.4 Test 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37


5.4.2 Rotation test 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38




5.5 Test 21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42


5.5.2 Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42




5.6 Test 22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46


5.6.2 Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.6.3 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

6 Test summary 51

A Drawings 53

A.1 Specimen and instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

A.2 Specimen and test setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

CONTENTS ix

B Test protocols 67

B.1 Test 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

B.2 Test 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

B.3 Test 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

B.4 Test 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

B.5 Test 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

B.6 Test 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

B.7 Test 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

B.8 Test 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

B.9 Test 21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

B.10 Test 22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

C Test evaluation 79

C.1 Test 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

C.1.1 Initial compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

C.1.2 Rotation test 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

C.1.3 Evaluation symmetrical loading . . . . . . . . . . . . . . . . . . . . . . . . 81

C.1.4 Evaluation asymmetrical loading . . . . . . . . . . . . . . . . . . . . . . . 82

C.2 Test 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

C.2.1 Initial Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

C.2.2 Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84



C.3 Test 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

C.3.1 Initial compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

C.3.2 Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88



Nomenclature 93

x CONTENTS

Chapter 1

Introduction

In the past decades precast concrete frames were developed using tendons to connect columns and

beams [1–3]. These systems showed favourable seismic behaviour, being able to avoid residual

deformations after an earthquake. Furthermore a model, the monolithic beam analogy, was

developed to describe the connection behaviour [4]. A similar system for timber was introduced

in New Zealand at the University of Canterbury [5–11]. A timber frame made of laminated

veneer lumber was post-tensioned, resulting in a good structural behaviour. Design proposals

were published [12–16] and buildings using the post-tensioned timber frames were constructed

[17].

Post-tensioned timber joints are also being studied at the Institute of Structural Engineering at

the ETH in Zurich. An innovative post-tensioned beam-column timber joint has been developed

using glued laminated timber (spruce) and local strengthening of the joint with hardwood (ash).

No further steel elements are required for the moment-resisting timber joint, only a single straight

tendon is placed in the middle of the beam. The developed post-tensioned beam-column timber

joint is characterised by a high degree of pre-fabrication and easy assemblage on site.

The moment-rotation-behaviour of the post-tensioned beam-column timber joint has extensively

been analysed with a series of static bending tests. The timber joint was loaded at the ends

of the beams in order to apply a moment to the connection (see figure 1.1). The tests were

conducted with different forces in the tendon, from 300 kN up to 700 kN. The bending tests

were performed with a load level, so that no failure perpendicular to the grain in the column

occurred.

A final bending test was conducted in order to study the failure mode of the post tensioned

timber beam-column joint. The vertical load on the beams was increased until the tendon-

elongation got so high that the test had to be aborted. The results of the bending tests on the

structural behaviour of the post-tensioned timber joint are presented herein.

2 Chapter 1. Introduction

Fig. 1.1: Post-tensioned timber joint

Chapter 2

Specimen and test setup

2.1 Material and dimensions

The test specimen consists of two beams and a column made of glulam. The glulam beams

are made of spruce except three lamellae, which are made of ash (see figure 2.1, grey parts are

made of ash). The column is also a hybrid made of spruce and ash. The hardwood is used in

areas, where high stresses perpendicular to the grain occur, namely in the connection between

the column and the beam. The strength and stiffness values of the materials are summarised in

table 2.1.

An unbonded tendon is attached both ends of the specimen. A thick steel plate is necessary at

the end of the beam for the load transmission from the tendon to the beam.

The shear force between beam and column is transferred via friction. By cutting a small opening

into the column a support was created for safety reasons in case the friction would not be

sufficient.

1.62 0.36 1.62

0.040.04

0.6

0.4

0.6

F F1.24

0.59

0.12

Fig. 2.1: Specimen and load application, all dimensions in [m]

The properties of the tendon are summarised in table 2.2

4 Chapter 2. Specimen and test setup

Tab. 2.1: Strength and stiffness properties in [MPa] for strength grade GL24h [18] and D40 [19]

Description Abbreviation Strength grade

GL24h D40

Compressive strength parallel to the grain fc,0,k 22 26

Compressive strength perpendicular to the grain fc,90,k 3 8.3

Modulus of elasticity parallel to the grain E0,mean 11000 13000

Modulus of elasticity perpendicular to the grain E90,mean 300 860

Shear modulus Gmean 500 810

Tab. 2.2: Tendon properties according to [20].

Description Abbreviation Y1770 4-06

Number of strands [-] N 4

Area cross section [mm2] Ap 600

Tendon length [mm] Lp 4200

Young’s Modulus [MPa] Ep 197000

Tensile strength [MPa] fp,k 1770

Applicable design load [kN] Pmax 850

2.2 Test setup

All the tests were performed at the ETH Zurich on a strong floor. The strong floor has several

spots where loads up to 1200 kN can be transferred into the floor.

A rigid steel frame was build for the tests (see figure 2.2). The frame consists of two columns

which are connected to the floor with high-strength pre-stressed bolts. The columns are con-

nected to a strong wall with two beams, assembled from steel profiles HEB 300. The specimen

is attached to the columns with profiles UPE 270.

The force is applied by two cylinders of the type Emmen cylinder 206 kN, which are connected

with a beam. The cylinders allow to apply a force of 412 kN on each side of the specimen. The

cylinders are connected to the same hydraulic pump, but can be controlled separately, so that

several load cases can be investigated. It is therefore possible to apply the load only on one

beam while the other one is unloaded. One beam can also be loaded to a certain value while

the second beam is loaded to a different value. One beam with two cylinders attached weighs

480 kg, which has to be accounted for in the analysis.

The tendon and the press are shown in figure 1.1 and figure 2.2. The press is positioned between

the steel plate and the anchorage of the tendon. The press allows to change the force in the

tendon. Several tests with different levels of post-tensioning force can therefore be executed.

Scaled drawings of the specimen and the test setup can be found in appendix A.

2.2. Test setup 5

left right

Fig. 2.2: Test setup and specification of the beam (left or right)

Fig. 2.3: Test setup CAD (without tendon)


2.3 Instrumentation

To investigate the structural behaviour of the post-tensioned timber connection several types of

measuring devices are being used:

� linear variable differential transformers (LVDTs)

� inclinometers

� pressure sensors

� hydraulic pumps

� load cell

All the abbreviations and the most important information are summarized in table 2.3. The

abbreviations will be used in the entire document.

Tab. 2.3: Measuring Equipment

Description Abbreviation Range Error

LVDT TK-10 WRV1. . . ± 10 mm 0.25 %

LVDT D6 WRH1. . . ± 5 mm 0.25 %

LVDT TK-25 Durch L Durch R ± 25 mm 0.25 %

Inclinometer IL1 IL2 IR1 IR2 ± 5 ◦ ± 0.01 ◦

Pressure sensor FSR 0.2-20N ± 2 %

Load cell KMD 0-1250kN unknown

2.3.1 Linear variable differential transformers

The LVDTs record the displacements between the column and the beams. The rotation of the

connection (or the beam) can be calculated from the recorded values. One LVDT is also attached

at the bottom of each beam to measure its deflection (figure 2.4). The LVDTs being used at

the column-beam interface are of the type Precisor TK-10 and RDP D6/05000A with a range

of 10 mm and 5 mm, respectively.

2.3. Instrumentation 7

0.040.28

0.04

WLV3

WLO2

WLV1

WLV2

WRV3

WRO2

WRV1

WRV4

WRV2

1.251.25

0.7

0.6

0.7

0.061.6

0.36

0.02

5

0.30

1 0.43

7 0.57

1

0.64

4

0.62

2

0.57

4

0.29

90.

029

Durch L Durch R

IL2 IL1IR1

IR2

1.60.06

LVDT

Inclinometer

Test specimen with instrumentationFront view1:20 [m]

Fig. 2.4: Instrumentation: LVDTs and inclinometers, all dimensions in [m]

Figure 2.5 shows the LVDTs attached at the beam. The aluminium plate is needed to measure

the actual deformation between the column an the beam. It is attached to the rigid test frame. If

there would be no plate, the measured deformation would correspond to the relative deformation

between the column and the beam, the deformation of the column itself would not be measured.

Fig. 2.5: LVDTs at the beam-column interface


2.3.2 Inclinometers

Two inclinometers of the type NS-5/P are positioned on top of each beam. These devices allow to

measure the inclination of the beams directly. The rotation in the connection can be calculated

from these values if the elastic inclination of the beam is subtracted. There are therefore two

ways to calculate the rotation, which leads to more reliable results.

2.3.3 Pressure sensors

Two pressure sensors of the type FSR 400 are used to estimate the moment of decompression.

Figure 2.6 shows the sensor and its single components. Two substrate layers with a spacer in

between are the main components. As soon as a force acts on the head of the sensor, the two

substrate layers are pressed together. If there is a contact between the substrate layers, the

sensor measures a voltage, which increases as the pressure on the head increases. If there is no

pressure and therefore no contact, the measured voltage is zero.

Since the maximal applicable load on the sensors is only 20 N, the contact between the pressure

sensors and the beam is made after a certain tendon force has already been applied. This reduces

the force on the sensor but has to be taken into account in the analysis.

Fig. 2.6: Pressure sensor FSR 400

The pressure sensors are only attached on the right beam, as can be seen in figure 2.7. The

pressure sensor is positioned right under the top edge of the beam and is connected to an

adjustable screw. The screw is necessary to create a clearly defined contact area. If the pressure

is zero, the point of decompression has been reached and a gap will start to open between the

beam and the column interface.

2.3.4 Hydraulic pump

Three hydraulic pumps are used for the tests. The main pump is from the manufacturer Amsler,

which is connected to the cylinders that are pulling the beams down.

Two more pumps of the type Bieri HP 2.2D−15110 are being used during the tests. One pump

is needed to pre-stress the tendon. The second one is being used for the asymmetrical loading,

where one beam is loaded to a constant value.

2.3. Instrumentation 9

Fig. 2.7: FSR at the connection interface

The oil pressure is measured for each press separately. These values are necessary to calculate

the forces in the cylinders and the tendon, respectively.

2.3.5 Load cell

A load cell of the type ForceCell BaMa 1250 is positioned between the tendon and the anchorage.

The load cell measures the force in the tendon in addition the the tendon force obtained from

the oil pressure.

Chapter 3

Test overview

3.1 Testing program

A total of 22 tests were performed at the ETH Zurich. The tests one to twelve are preliminary

tests, which where performed to calibrate the measuring equipment and will not be presented

herein. Test 19 is not considered due to an error in the hydraulic system.

Tab. 3.1: Performed tests

Test No. Tendon force [kN] Load application Applied load [kN]

13 518 B,C,O 80

14 416 B,C,O 60

15 612 B,C,O 80

16 325 B,C,O 50

17 683 B,C,O 70

18 560 B,C,O 80

20 462 B,C,O 75

21 554 B,C,O 90

22 557 B 157

The tests were performed with different post-tensioning-forces and different kind of load appli-

cations. The maximal applied load varies from test to test. Three different load applications

were performed (figure 3.1):

� (B) Load is applied on both beams, symmetric loading. Both beams are loaded and

unloaded at the same time.

� (O) Load is applied on one beam, asymmetric loading. The second beam remains un-

loaded.

� (C) Combined load application. One beam is pre-loaded to a certain, constant value. The

second beam is then loaded and unloaded to different (higher) values.

12 Chapter 3. Test overview

By applying the load only on one beam, a load combination is generated, which is closer to a

horizontal load on a post-tensioned timber frame (earthquake, wind loads).

The analysis often refers to a load level (for example 80 kN). This values always corresponds

to the peak value of a load cycle. I.e. in the test shown in figure 3.1 the value 80 kN would

correspond to the peak at 1600 sec.

3.1.1 Test protocol

All the tests, except test 22, consist of the three parts:

� 1. Symmetrical loading, 3-4 loading and unloading cycles.

� 2. Asymmetrical loading, right beam under constant load. The right beam is loaded to a

certain value, the left beam is then loaded to 40 kN, unloaded and reloaded again up to

60 kN. This is repeated with different loads levels on the right beam.

� 3. Asymmetrical loading, left beam under constant load. The left beam is loaded to a

certain value, the right beam is then loaded to 40 kN, unloaded and reloaded again up to

60 kN. This is repeated with different loads levels on the left beam.

The force-time-diagram for test 13 can be seen in figure 3.1. The symmetric loading ends at

t = 1700 sec. The asymmetric loading with constant load on the right beam starts at t = 1700 sec

and ends at t = 3100 sec. At the end of the test, the asymmetric loading with a constant load

on the left beam is performed.

It shall be noted, that the loads are not exactly constant. Since one beam is loaded more

than the other one, the beam with the heavier load is being pulled down, the beam with less

load would like to move upwards, but is restrained by the cylinders. Therefore the load in the

cylinders increases slightly.

500 1500 2500 3500 45000

20

40

60

80

100

Time [sec]

Load

[kN

]

symmetricload left beamload right beam

Fig. 3.1: Load-time diagram for a typical test

3.2. Testing procedure 13

Detailed protocols for all the perfromed tests can be found in appendix B.

3.2 Testing procedure

The same procedure was applied for all the tests. The following steps were always performed in

the following order:

� Step 1: Starting the computer for the measuring equipment. The beams are temporarily

supported, the force in the tendon is about 5 to 10 kN

� Step 2: The force in the tendon is increased up to 100 kN

� Step 3: The supports under the beams are being removed

� Step 4: The force in the tendon is increased up to 2/3 of the value to be achieved. The

pressure sensors are connected to the beam by adjusting the screw

� Step 5: The tendon force is being increased up to the value to be achieved

� Step 6: The steel beams with the cylinders are mounted on the specimen (first on the right

beam, then on the left beam). The cylinders are connected to the strong floor

� Step 7: Performing the tests (loading and unloading cycles)

� Step 8: Removing the cylinders (first from the left beam, then from the right beam)

� Step 9: Reducing the force in the tendon to 100 kN. Mounting the supports under the

beams of the specimen

� Step 10: Reducing the force in the tendon to approximately 5 to 10 kN

14 Chapter 3. Test overview

Chapter 4

Experimental analysis - equations

4.1 Initial compression

The beams are being pressed against the column when force is applied on the tendon. This leads

to a initial compression in the interface, which has to be estimated. It is therefore essential, that

the measuring equipment is recording, before load is applied on the tendon. Figure 4.1 shows

the LVDTs at the beam-column interface during pre-stressing the tendon.

−1 −0.5 0 0.50

100

200

300

400

500

600

Displacement [mm]

P [k

N]

WLOWL1WL2WL3

−1 −0.5 0 0.50

100

200

300

400

500

600

Displacement [mm]

P [k

N]

WROWR1WR2WR3WR4

Fig. 4.1: Compression during pre-stressing the tendon

The displacements recorded by the LVDTs are linear for a force greater than 100 kN. At the

beginning of pre-stressing the tendon, the recorded displacements are not linear, which is due

to a rotation of the beams. The beams are supported at the beginning of each test, preventing

it from falling down (see section 3.2). The beams are not perfectly horizontal, while being

supported. By applying the force on the tendon, the beams are rotating at the beginning before

they are being pressed into the column.

In order to estimate the amount of compression, the displacements recorded by the LVDTs are

approximated linearly between 100 kN and the maximal force in the tendon. The straight lines

are then shifted, so that they go through the origin of the coordinate system. This procedure

is supposed to remove the rotation of the beam from the data and has to be done for each set

16 Chapter 4. Experimental analysis - equations

of LVDTs separately. The values at the initial pre-stressing-force (for figure 4.1 the value would

be at approximately 520 kN) is then read from the diagram. The values are of course different

for the different LVDTs. To estimate an initial compression the mean value is calculated.

This value for the initial compression is then applied to all LVTDs, meaning that at the beginning

of each test the beam is compressed uniformly into the column. Figure 4.2 shows the LVDTs

plotted against their position (measured from the lower edge of the beam) for different load

levels applied to the beam. After applying the force on the tendon the beam is being pressed

into the column by approximately 0.4 mm. By loading the beam with 20 kN up to 80 kN the

beam is rotating. The lines connecting the LVDTs (circles in figure 4.2) can be interpreted as

the cross section of the beam at the interface.

−1 −0.5 0 0.5 1 1.5 2 2.5 30

100

200

300

400

500

600

Displacment [mm]

Pos

ition

[mm

]

0 kNinterp.20kNinterp.40kNinterp.60 kNinterp.80 kNinterp.

Fig. 4.2: Measured displacements with LVDTs for different load levels. I.e. F = 0 kN after post-

tensioning, F = 20 kN applied load on the beam 20 kN, etc.

It is important to mention, that by defining a uniform compression, the calculated rotation is

not altered, since the rotation only depends on the incremental change in displacements of the

LVDTs. The initial compression only influences the moment of decompression. It is possible to

check if the uniform compression was chosen accurately: If the moment of decompression does

not correspond to the results of the pressure sensors, the compression was selected too low or too

high, depending if the decompression occurs at a too low load or a too high load, respectively.

4.2 Key variables

4.2.1 LVDTs

The LVDTs are attached at the beams on both sides. For the experimental analysis the average

value from the LVDTs at the same position are used, i.e. for the two LVDTs positioned in the

middle of the left beam:

4.2. Key variables 17

WL2 =WLV 2 +WLH2

2(4.1)

4.2.2 Rotation

The rotation between the column (see figure 4.3) and the beam is the most important parameter

that has to be estimated. One possibility is to use the LVDTs and calculate the rotation, another

possibility is to use the inclinometers to calculate the rotation in the connection interface. Both

ways are described in the following.

Calculation with LVDTs

The rotation is calculated by using the upper LVDTs (WLO) and the ones in the middle of the

beam (WL2). By assuming that the section remains plain, the rotation can be calculated as

follows:

θ =WLO −WL2

f(4.2)

With f defining the distance between the LVDTs WLO and WL2.

Since there are eight LVDTs mounted at the left interface and ten LVDTs at the right interface

there is a more accurate way to calculate the rotations. The position of each LVDT with

reference to the lower edge of the beam is known. By assuming that the section remains plain,

the following three equations can be written (as an example only for the left beam, see figure

2.4):

yWLO = θ · (622− x) = θ · 622− θ · x = θ · 622− n (4.3)

yWL1 = θ · (574− x) = θ · 574− θ · x = θ · 574− n (4.4)

yWL2 = θ · (299− x) = θ · 299− θ · x = θ · 299− n (4.5)

The values correspond to the position of the LVDTs, measured in mm from the lower edge of

the beam. The value y is the mean measured deformation for each set of LVDTs. The LVDTs

at the lower edge of the beam are not taken into account, since they are in the compressive zone,

where the deformations may not be linear (due to embedment failure in the column).

The unknown variables are the rotation θ and the neutral axis depth x, which have to be

calculated.


With two unknown variables and three equations (respectively four for the right beam) the

problem can be solved. The equations (4.3)-(4.5) can be transposed into:

yWLO

yWL1

yWL2

=

[θ

n

]·

622 −1

574 −1

299 −1

(4.6)

The variables θ and n can be calculated with a right division. The value for x is calculated from

n (which would be a displacement at the lower edge of the column) by a back substitution:

n = x · θ → x =n

θ(4.7)

Calculation with inclinometers

The rotation at the interface is determined by using the inclinometers, which are attached on

top of each beam. The inclinometers measure the inclination of the beam during the tests.

However, the rotation in the interface does not correspond exactly to the measured inclination,

since the elastic inclination of the beam is also measured. Thus, the recorded values have to be

corrected. The inclination of the beam can be calculated as follows:

w′ =F · Lcant

EI

[xincl −

x2incl2 · Lcant

](4.8)

The position of the inclinometers (xincl), measured from the interface, is equal to 200 mm for

the first set of inclinometers and 900 mm for the second set (see figure 2.4).

Comparison of rotations

The rotations calculated with the LVDTs and the inclinometers can be verified with the measured

deflection of the beams. The rotations have to be multiplied with the length of the beam in

order to get a deflection. After adding the elastic deflection of the beam, the obtained value

should correspond to the measured deflection under the beam:

wcalc = θ · Lcant (4.9)

wcalc + wel,beam = θ · Lcant +F · L3

cant

E · I≈ wmeasured (4.10)

If the difference between the measured and calculated deflection is negligible, the rotations cal-

culated from the LVDTs and the inclinometers are considered as validated and usable. This

check is performed for every single test, since the rotation is the key variable needed to describe


the structural behaviour of the connection.

In case of the asymmetrical loading there is an additional term, which has to be calculated.

The two different loads acting on the beam lead to a rotation of the column. This rotation can

be calculated as follows:

θasymmetric =Masymmetric,col · Lcant

8 · E · Icol(4.11)

With Masymmetric,col being the resulting moment due to the two different loads acting on the

column. This rotation influences the measured deflections of the beams. If the rotations are

estimated with the inclinometers the rotation of the column is included, since the inclinometers

measure the absolute inclination according to a horizon. If the rotation is estimated with the

LVDTs the rotation is also included, since the reference point is the testing frame, which is

fixed and does not move during the test. Since the focus is on the structural behaviour of the

beam-column interface, the deflection due to column rotation has to be subtracted from the

measured ones under the beam:

wasymmetric = θasymmetric · Lcant (4.12)

4.2.3 Moment

The structural behaviour of the connection is best described using the moment in the connection

instead of the load applied to the beam. The moment can be calculated with:

M = F · Lcant (4.13)

It is useful to plot the moment against the rotation in order to evaluate the tests, since the two

parameters correspond to the characteristics of a rotational spring and are therefore widely used

and comprehended.

4.2.4 Decompression

The moment of decompression can be estimated with the pressure sensors. As soon as there is

no pressure, the sensors will loose contact to the beam and therefore not measure any voltage.

Figure 4.4 shows the voltage of the pressure sensor as a function of the load on the beam. The

voltage of the sensor is zero that at a load of approximately 20 kN. This would mean, that the

moment of decompression is reached at a load of 20 kN on the beam.

Since the sensor is not exactly positioned on the top edge of the beam but slightly lower (10 mm),

the moment of decompression is estimated to occur at a value of 0.5 V.


11

11

11

11

11

11.31°

0.11

x

inf

Fig. 4.3: Definition of the rotation θ, maximal compressive stresses σinf and the neutral axis depth x

at the connection interface

As already mentioned in section 2.3.3 and 3.2, the pressure sensors are not activated from the

beginning on, in order to protect the sensitive sensors. If the tendon force to be achieved is

600 kN the pressure sensors are activated at a tendon force of 400 kN, corresponding to 2/3 of

the value to be achieved. This has to be taken into account during the analysis, since the sensors

do not experience the full pressure of the beam. This means, that the moment of decompression

would be measured too early. In order to take into account this influence a factor is introduced,

which interpolates the pressure up to the target value (600 kN in the mentioned case):

fFSR =P0

P0 − PFSR=

600kN

600kN − 400kN= 3 (4.14)

If decompression would occur at an applied load of 20 kN, the value would be fFSR-times the

measured one. In the example shown in figure 4.4 decompression would actually occur at 60 kN.

Since the deformations in the column remain elastic during pre-stressing, the linear interpolation

should not lead to any mistakes during the analysis.

In addition to the pressure sensors a 0.2 mm thick feeler gauge was used to check for the

gap opening between the column-beam interface during the tests. As soon as the feeler gauge

could be pushed between the column and beam, a note was made in the testing protocol. This

information can be used to check the moment of decompression.


0 20 40 60 80 1000

1

2

3

4

5

Load [kN]

Vol

tage

[V]

Fig. 4.4: Recorded voltage from the pressure sensor while applying a load F on the beams

4.2.5 Neutral axis depth from LVDTs

The neutral axis depth can be estimated with two LVDTs directly, instead of calculating it with

the linear regression as described in section 4.2.2. By assuming a plain section in the interface,

the neutral axis depth can be estimated as follows:

x = 622mm− WLO

θ(4.15)

4.2.6 Stresses in the column

The stresses in the column (perpendicular to the grain) are very important for the design. With

the equilibrium of forces and the assumption of a linear-elastic stress distribution it is possible

to calculate the maximal compressive stresses in the interface (figure 4.3).

σinf =2P

x · b(4.16)

The width b of the beam is known, the force in the tendon (P) is being measured during the

tests. The neutral axis depth x is estimated according to section 4.2.2.

Equation (4.16) is only valid after decompression. Until decompression the following equation

has to be used in order to calculate the maximal stresses in the column:

σinf =P

A+M

W(4.17)

Chapter 5

Experimental analyis - test

evaluation

5.1 Test 13

5.1.1 Initial compression

The initial compression is estimated as described in section 4.1. The procedure is performed for

both beams separately (see figure 5.1). The compression is not linear at the beginning, since both

beams are rotating. As soon as the force in the tendon reaches 100 kN the compression is linear.

The small deviation, which is visible at 300 kN is due to a break during the post-tensioning

process. The pressure sensors are connected during this break. This deviations occurred during

each test as soon as the post-tensioning process was interrupted. The reason is that the pump

looses some oil, therefore the pressure in the system is reduced, which leads to a small loss in

post-tensioning force.

−1 −0.5 0 0.50

100

200

300

400

500

600

Displacement [mm]

P [k

N]

WLOWL1WL2WL3

−1 −0.5 0 0.50

100

200

300

400

500

600

Displacement [mm]

P [k

N]

WROWR1WR2WR3WR4

Fig. 5.1: Initial compression test 13

The initial compression for the left beam is:

24 Chapter 5. Experimental analyis - test evaluation

wcomp,left = 0.31mm (5.1)

For the right beam this value is slightly higher:

wcomp,right = 0.34mm (5.2)

These values are approximations, as the LVDTs measure the initial compression at the outer

perimeter of the beam.

The theoretical compression can also be calculated using the symmetry of the system:

wcomp,calc =P0/A

E90· bs

2=

518000/(600 · 400)

860· 280

2= 0.35mm (5.3)

The value is slightly higher than the estimated ones, especially for the left interface.

5.1.2 Rotation

The rotations have to be checked for errors, since all the parameters are expressed according to

the rotations at the interfaces. The procedure to check the rotations is described in section 4.2.2.

The procedure is very simple, the rotations are multiplied with the beam length. This value

should then correspond to the measured deflection of the beam, taking into account the elastic

deformation of the beam. The results for the two beams are shown in figure 5.2. The calculated

- both from the linear regression of the LVDTs and the inclinometers - rotations correspond well

to the measured ones, the results are basically identical.

0 1 2 3 4 5 6 7 8 9 100

20

40

60

80

100

120

Deflection beam [mm]

M [k

Nm

]

regression leftinclinometer leftmeasured

0 1 2 3 4 5 6 7 8 9 100

20

40

60

80

100

120


M [k

Nm

]

regression rightinclinometer rightmeasured

Fig. 5.2: Deflection beams test 13

5.1. Test 13 25

5.1.3 Evaluation symmetrical loading

All the key variables are plotted as a function of the rotation in figure 5.3.

0 1 2 3 4 5 6 7 8

x 10−3

0

20

40

60

80

100

120

θ [−]

M [k

Nm

]

leftright

0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

700

θ [−]

P [k

N]

leftright

0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

θ [−]

x [m

m]

leftrightFSR

0 1 2 3 4 5 6 7 8

x 10−3

0

2

4

6

8

10

θ [−]

σ inf [N

/mm

2 ]

leftright

Fig. 5.3: Evaluation test 13

The moment-rotation diagram shows, that the two connections behave similar until the moment

in the interface reaches a value of approximately 70 kNm. The two sides behave differently after

that; the right connection shows a stiffer behaviour, whereas the left connection softens with

increasing moment.

The tendon force (P) remains constant during the test. The beginning of an increase is noticeable

at a rotation of 5 mrad, which would lead to the conclusion, that the gap has reached the position

of the tendon.

The neutral axis depth (x) is constant at a value of 600 mm up to a rotation of 1.2 mrad. Then

it starts to decrease, which means that the moment of decompression is at 1.2 mrad or at a

moment of approximately 45 kNm. During the test a feeler gauge was used to check whether

a gap has opened or not. A gap could be noticed at a load of 40 kN, which corresponds to a


moment of 50 kNm. The circle in the diagram shows the moment of decompression according

to the pressure sensor (FSR). The neutral axis depth gets smaller than 300 mm, which means

that the gap reaches the position of the tendon. This observation could also be made with the

tendon force.

The compressive stresses go up to 9 MPa, which is outside the expected elastic range. However,

no plastic deformations where observed after the test. A measurement value leap is noticeable at

a rotation of 1.2 mrad (moment of decompression) for the left interface. This is due to the way

the stresses are calculated: before decompression, equation (4.17) is used, after decompression

equation (4.16). If the initial compression is chosen poorly, a leap will occur, since the stresses

at decompression have different values for the two equations.

By increasing the initial compression for the left interface, the leap can be reduced (see figure

5.4).

0 1 2 3 4 5 6 7 8

x 10−3

0

20

40

60

80

100

120

θ [−]

M [k

Nm

]

leftright

0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

700

θ [−]

P [k

N]

leftright

0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

θ [−]

x [m

m]

leftrightFSR

0 1 2 3 4 5 6 7 8

x 10−3

0

2

4

6

8

10

θ [−]

σ inf [N

/mm

2 ]

leftright

Fig. 5.4: Modified evaluation test 13

5.1. Test 13 27

5.1.4 Evaluation asymmetrical loading - constant load on right beam

Figure 5.5 shows the deflections under the left beam during the test with a constant load on the

right beam. It is noticeable, that the rotation calculated from the LVDTs leads to better results

than using the rotations calculated from the inclinometers.

0 1 2 3 4 5 60

10

20

30

40

50

60

70

80

Displacement [mm]

M [k

Nm

]

regressionmeasured

0 1 2 3 4 5 60

10

20

30

40

50

60

70

80

Displacement [mm]

M [k

Nm

]

inclinometermeasured

Fig. 5.5: Deflection beam test 13, constant load on the right beam

The test evaluation focuses on the moment-rotation behaviour and the compressive zone (figure

5.6). The force in the tendon and the stresses are not of interest, since the applied load for the

asymmetrical loading is always smaller as the load applied for the symmetrical loading.

The moment-rotation-diagram shows a reduction of the initial stiffness of the connection with

decreasing load on the left beam. This effect is due to shear deformations in the column, which

only occur during asymmetrical loading.

The moment of decompression occurs basically at the same rotation compared with the sym-

metric loading.

0 1 2 3 4 5 6 7 8

x 10−3

0

20

40

60

80

100

120

θ [−]

M [k

Nm

]

symmetricr=20kNr=40kNr=0kN

0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

θ [−]

x [m

m]


Fig. 5.6: Evaluation test 13, constant load on the right beam


5.1.5 Evaluation asymmetrical loading - constant load on left beam

Figure 5.7 shows the deflections of the right beam during the test with a constant load on the left

beam. The rotation calculated from the LVDTs leads to better results than using the rotations

calculated from the inclinometers.

0 1 2 3 4 5 60

10

20

30

40

50

60

70

80

Displacement [mm]

M [k

Nm

]

regressionmeasured

0 1 2 3 4 5 60

10

20

30

40

50

60

70

80

Displacement [mm]

M [k

Nm

]


Fig. 5.7: Deflection beam test 13, constant load on the left beam

The moment-rotation-diagram (figure 5.8) shows a reduction of the initial stiffness of the con-

nection with decreasing load on the right beam. This effect is due to shear deformations in the

column, which only occur during asymmetrical loading.


metric loading. However, this could not be verified with the feeler gauge during the tests. The

gap opened later compared to the symmetric loading. i.e. for the case where there is not load

on the right beam (r=0 kN) gap opening occurred at 44-45 kN, which is slightly later than for

the symmetric loading.

0 1 2 3 4 5 6 7 8

x 10−3

0

20

40

60

80

100

120

θ [−]

M [k

Nm

]

symmetricl=20kNl=40kNl=0kN

0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

θ [−]

x [m

m]


Fig. 5.8: Evaluation test 13, constant load on the left beam

5.2. Test 14 29

5.2 Test 14


The initial compression is estimated according to section 4.1.

−1 −0.5 0 0.50

100

200

300

400

500

600

Displacement [mm]

P [k

N]

WLOWL1WL2WL3

−1 −0.5 0 0.50

100

200

300

400

500

600

Displacement [mm]

P [k

N]

WROWR1WR2WR3WR4






The theoretical compression is calculated as follows:

wcomp,calc =P0/A

E90· bs

2=

416000/(600 · 400)

860· 280

2= 0.28mm (5.6)

The value corresponds to the estimated ones for the two beams.

5.2.2 Rotation

The result for the verification of the rotation for the two beams is shown in figure 5.10. The

calculated - both from the linear regression of the LVDTs and the inclinometers - rotations

correspond well to the measured ones.


0 1 2 3 4 5 6 7 8 9 100

20

40

60

80

100

120


M [k

Nm

]


0 1 2 3 4 5 6 7 8 9 100

20

40

60

80

100

120


M [k

Nm

]




0 1 2 3 4 5 6 7 8

x 10−3

0

20

40

60

80

100

120

θ [−]

M [k

Nm

]

leftright

0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

700

θ [−]

P [k

N]

leftright

0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

θ [−]

x [m

m]

leftrightFSR

0 1 2 3 4 5 6 7 8

x 10−3

0

2

4

6

8

10

θ [−]

σ inf [N

/mm

2 ]

leftright


5.2. Test 14 31

All the key variables are plotted in figure 5.11. The moment-rotation diagram shows that the

two connections behave similar until the moment in the interface reaches a value of approxi-

mately 50 kNm. The two sides behave differently after that; the right connection shows a stiffer

behaviour, whereas the left connection softens with increasing moment.

The tendon force (P) remains constant during the test. The beginning of an increase is notice-

able at a rotation of 4 mrad, which would lead to the conclusion, that the gap has reached the

position of the tendon.






to the pressure sensor (FSR). The neutral axis depth gets smaller than 300 mm, which means

that the gap reaches the position of the tendon.

The stresses reach 8 MPa, which is still in the expected elastic range.

5.2.4 Evaluation symmetrical loading - constant load on right beam

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

Displacement [mm]

M [k

Nm

]

regressionmeasured

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

Displacement [mm]

M [k

Nm

]



Figure 5.12 shows the deflections of the left beam during the test with a constant load on the

right beam. The rotations calculated from the LVDTs lead to better results than using the

rotations calculated from the inclinometers.

It can be seen from the moment-rotation-diagram (figure 5.13), that the initial stiffness of the

connection reduces with decreasing load on the right beam.

The moment of decompression occurs at the same rotation compared with the symmetric loading.


0 1 2 3 4 5 6 7 8

x 10−3

0

20

40

60

80

100

120

θ [−]

M [k

Nm

]


0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

θ [−]

x [m

m]




Figure 5.14 shows the deflections of the right beam during the test with a constant load on

the left beam. The rotation calculated from the LVDTs leads to better results than using the


0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

Displacement [mm]

M [k

Nm

]

regressionmeasured

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

Displacement [mm]

M [k

Nm

]




nection with decreasing load on the left beam). This effect is due to shear deformations in the



metric loading. This could however not be verified with the feeler gauge during the tests. The

gap opened later compared to the symmetric loading. I.e. for the case where there is not load

on the right beam (r=0 kN) gap opening occurred at 35 kN, which is slightly later than for the

symmetric loading.

5.3. Test 15 33

0 1 2 3 4 5 6 7 8

x 10−3

0

20

40

60

80

100

120

θ [−]

M [k

Nm

]


0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

θ [−]

x [m

m]



5.3 Test 15


The initial compression is estimated according to section 4.1. The procedure is performed for

both beams separately (see figure 5.16).

−1 −0.5 0 0.50

100

200

300

400

500

600

Displacement [mm]

P [k

N]

WLOWL1WL2WL3

−1 −0.5 0 0.50

100

200

300

400

500

600

Displacement [mm]

P [k

N]

WROWR1WR2WR3WR4







The theoretical compression can also be calculated:

wcomp,calc =P0/A

E90· bs

2=

612000/(600 · 400)

860· 280

2= 0.42mm (5.9)

The value is higher than the estimated ones for the two beams.

5.3.2 Rotation test 15

The result of the verification of the rotation for the two beams is shown in figure 5.17. The

calculated - both from the linear regression of the LVDTs and the inclinometers - rotations

correspond well to the measured ones, the results are basically identical.

0 1 2 3 4 5 6 7 8 9 100

20

40

60

80

100

120


M [k

Nm

]


0 1 2 3 4 5 6 7 8 9 100

20

40

60

80

100

120


M [k

Nm

]




All the key variables are plotted in figure 5.18. The moment-rotation diagram shows that the

two connections behave similar. The right connection shows a bit a stiffer behaviour than the

left one, but the difference is smaller than for the previous tests. This could be due to the higher

force in the tendon.

The tendon force (P) remains constant during the test.

The neutral axis depth (x) is constant at a value of 600 mm up to a rotation of 1.3 mrad. Then it

starts to decrease, which means that the moment of decompression is at 1.3 mrad or at a moment

of approximately 60 kNm. The circle in the diagram shows the moment of decompression

according to the pressure sensor (FSR). The comparison shows, that the decompression probably

occurs slightly later than estimated with the LVDTs. The neutral axis depth does not get

smaller than 300 mm, which means that the gap does not reach the position of the tendon. This

observation could also be made with the tendon force.

The stresses go up to 8 MPa, which is still in the expected elastic range.

5.3. Test 15 35

0 1 2 3 4 5 6 7 8

x 10−3

0

20

40

60

80

100

120

θ [−]

M [k

Nm

]

leftright

0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

700

θ [−]

P [k

N]

leftright

0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

θ [−]

x [m

m]

leftrightFSR

0 1 2 3 4 5 6 7 8

x 10−3

0

2

4

6

8

10

θ [−]

σ inf [N

/mm

2 ]

leftright



0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

90

100

Displacement [mm]

M [k

Nm

]

regressionmeasured

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

90

100

Displacement [mm]

M [k

Nm

]





right beam. The rotation calculated from the LVDTs leads to better results than using the


The moment-rotation-diagram shows a reduction of the initial stiffness with decreasing load on

the right beam. This effect is due to shear deformations in the column, which only occur during

asymmetrical loading.

The moment of decompression happens at the same rotation compared with the symmetric

loading.

0 1 2 3 4 5 6 7 8

x 10−3

0

20

40

60

80

100

120

θ [−]

M [k

Nm

]


0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

θ [−]

x [m

m]




Figure 5.21 shows the deflections of the right beam during the test with a constant load on the

left beam.

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

90

100

Displacement [mm]

M [k

Nm

]

regressionmeasured

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

90

100

Displacement [mm]

M [k

Nm

]



5.4. Test 17 37

The initial stiffness of the connection reduces with decreasing load on the right beam, as can be

seen in the moment-rotation-diagram (figure 5.22).

The moment of decompression occurs at the same rotation compared with the symmetric loading.

0 1 2 3 4 5 6 7 8

x 10−3

0

20

40

60

80

100

120

θ [−]

M [k

Nm

]


0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

θ [−]x

[mm

]



5.4 Test 17



−1 −0.5 0 0.50

100

200

300

400

500

600

700

Displacement [mm]

P [k

N]

WLOWL1WL2WL3

−1 −0.5 0 0.50

100

200

300

400

500

600

700

Displacement [mm]

P [k

N]

WROWR1WR2WR3WR4







These values are approximations, also since the LVDTs measure the initial compression at the

outer perimeter of the beam.

The theoretical compression can be calculated as follows:

wcomp,calc =P0/A

E90· bs

2=

683000/(600 · 400)

860· 280

2= 0.46mm (5.12)

The value is higher than the estimated ones for the two beams.

5.4.2 Rotation test 17

The result for the two beams is shown in figure 5.24. The calculated - both from the linear

regression of the LVDTs and the inclinometers - rotations are slightly underestimating the

measured deflections. The results for the LVDTs and inclinometers are identical though.

0 1 2 3 4 5 6 7 8 9 100

20

40

60

80

100

120


M [k

Nm

]


0 1 2 3 4 5 6 7 8 9 100

20

40

60

80

100

120


M [k

Nm

]



5.4. Test 17 39


0 1 2 3 4 5 6 7 8

x 10−3

0

20

40

60

80

100

120

θ [−]

M [k

Nm

]

leftright

0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

700

θ [−]P

[kN

]

leftright

0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

θ [−]

x [m

m]

leftrightFSR

0 1 2 3 4 5 6 7 8

x 10−3

0

2

4

6

8

10

θ [−]

σ inf [N

/mm

2 ]

leftright


All the key variables are plotted as a function of the rotation in figure 5.25. The moment-rotation

diagram shows that the two connections behave similar, no difference is noticeable. It seems,

that with increasing force in the tendon the two connection behave more similar.

The tendon force (P) remains constant during the test. No elongation of the tendon can be

noticed.






to the pressure sensor (FSR).





right beam. It is noticeable, that the rotation calculated from the LVDTs seem to lead to slightly

smaller displacements than measured.

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

Displacement [mm]

M [k

Nm

]

regressionmeasured

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

Displacement [mm]

M [k

Nm

]



It is noticeable from the moment-rotation-diagram (figure 5.27), that the initial stiffness of the

connection gets smaller with decreasing load on the right beam. This effect is due to shear

deformations in the beam, which only occur during asymmetrical loading.

The moment of decompression happens basically at the same time compared with the symmetric

loading.

0 1 2 3 4 5 6 7 8

x 10−3

0

20

40

60

80

100

120

θ [−]

M [k

Nm

]


0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

θ [−]

x [m

m]





nection with decreasing load on the left beam. This effect is due to shear deformations in the


5.4. Test 17 41

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

Displacement [mm]

M [k

Nm

]

regressionmeasured

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

Displacement [mm]

M [k

Nm

]



The moment of decompression occurs at the same rotation compared with the symmetric load-

ing. This could however not be verified with the feeler gauge during the tests. The gap opened

later compared to the symmetric loading. I.e. for the case where there is not load on the right

beam (r=0 kN) gap opening occurred at 49 kN, which is a bit later than for the symmetric

loading.

0 1 2 3 4 5 6 7 8

x 10−3

0

20

40

60

80

100

120

θ [−]

M [k

Nm

]


0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

θ [−]

x [m

m]




5.5 Test 21


−1 −0.5 0 0.50

100

200

300

400

500

600

Displacement [mm]

P [k

N]

WLOWL1WL2WL3

−1 −0.5 0 0.50

100

200

300

400

500

600

Displacement [mm]

P [k

N]

WROWR1WR2WR3WR4


The decompression for both beams can be estimating with a linear regression as described in

section 4.1. The initial compression for the left beam is:




The theoretical compression can be calculated as follows:

wcomp,calc =P0/A

E90· bs

2=

554000/(600 · 400)

800· 280

2= 0.38mm (5.15)

The value is slightly higher than the estimated ones for the two beams.

5.5.2 Rotation


the rotation of the interface. The procedure to check the rotations is described in section 4.2.2.

The calculated - both from the linear regression of the LVDTs and the inclinometers - rotations

correspond well to the measured ones, the results are basically identical.

5.5. Test 21 43

0 1 2 3 4 5 6 7 8 9 100

20

40

60

80

100

120


M [k

Nm

]


0 1 2 3 4 5 6 7 8 9 100

20

40

60

80

100

120


M [k

Nm

]




0 1 2 3 4 5 6 7 8

x 10−3

0

20

40

60

80

100

120

θ [−]

M [k

Nm

]

leftright

0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

700

θ [−]

P [k

N]

leftright

0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

θ [−]

x [m

m]

leftrightFSR

0 1 2 3 4 5 6 7 8

x 10−3

0

2

4

6

8

10

12

θ [−]

σ inf [N

/mm

2 ]

leftright



All the key variables are plotted in figure 5.32. The moment-rotation diagram shows, that the

two connections behave similar until the moment in the interface reaches a value of approxi-

mately 80 kNm. The two sides behave differently after that; the right connection shows a stiffer

behaviour, whereas the left connection is softer.

The tendon force (P) remains constant during the test. The beginning of an increase is notice-

able at a rotation of 5 mrad, which would lead to the conclusion, that the gap has reached the

position of the tendon.






to the pressure sensor (FSR). The comparison shows, that the decompression happens a later

than estimated with the LVDTs.

The stresses go up to 11 MPa, which is outside the estimated elastic range. However, no residual

deformations could be observed after the test. A measurement leap occurred at a rotation of

1.1 mrad (moment of decompression). This is due to the way the stresses are calculated: Before

decompression, equation 4.12 is used, after decompression equation 4.11.


0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

90

100

Displacement [mm]

M [k

Nm

]

regressionmeasured

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

90

100

Displacement [mm]

M [k

Nm

]




right beam. It is noticeable, that the rotation calculated from the LVDTs leads to better results


It is noticeable from the moment-rotation-diagram, that the initial stiffness of the connection

reduces with decreasing load on the right beam.

The moment of decompression occurs basically at the same roatation compared with the sym-

metric loading.

5.5. Test 21 45

0 1 2 3 4 5 6 7 8

x 10−3

0

20

40

60

80

100

120

θ [−]

M [k

Nm

]


0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

θ [−]

x [m

m]




Figure 5.35 shows the deflections of the right beam during the test with a constant load on the

left beam. It is noticeable, that the rotation calculated from the LVDTs leads to better results


0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

90

100

Displacement [mm]

M [k

Nm

]

regressionmeasured

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

90

100

Displacement [mm]

M [k

Nm

]




nection with decreasing load on the left beam. This effect is due to shear deformations in the


The moment of decompression occurs at the same rotation compared with the symmetric load-

ing. This could however not be verified with the feeler gauge during the tests. The gap opened

later compared to the symmetric loading. I.e. for the case where there is not load on the right

beam (r=0 kN) gap opening occurred at 42 kN, which is a bit earlier than for the symmetric

loading.


0 1 2 3 4 5 6 7 8

x 10−3

0

20

40

60

80

100

120

θ [−]

M [k

Nm

]


0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

θ [−]

x [m

m]



5.6 Test 22


−1 −0.5 0 0.50

100

200

300

400

500

600

Displacement [mm]

P [k

N]

WLOWL1WL2WL3

−1 −0.5 0 0.50

100

200

300

400

500

600

Displacement [mm]

P [k

N]

WROWR1WR2WR3WR4


The decompression for both beams can be estimating with a linear regression as described in

section 4.1. The initial compression for the left beam is:




The theoretical compression can also be calculated as follows:

5.6. Test 22 47

wcomp,calc =P0/A

E90· bs

2=

557000/(600 · 400)

860· 280

2= 0.38mm (5.18)

The value is slightly higher than the estimated ones for the two beams.

5.6.2 Rotation

The rotations during test 22 reached very large values compared to all other tests. The LVDTs

at the beam-column interface had to be re-adjusted and some of them reached their measuring

range. This was not noticed during the test, which means that the rotations can not be estimated

from the LVDTs. The rotations for test 22 are estimated from the inclinometers, according to

section 4.2.2.

The LVDTs being out of range also caused a problem with the neutral axis depth and the

compressive stresses, which are all calculated based on the measured values of the LVDTs (see

section 4.2.2 and 4.2.6). To get reasonable values for the missing measurements of the defor-

mations in the connection interfaces, the values are re-constructed with the rotations from the

inclinometer:

WRO = θinclinometer · dWRO−WR3 + |WR3| (5.19)

By using equation (5.19) it is assumed that the cross-sections remain plain. It has to be men-

tioned, that this correction only had to be applied on the left beam and only for moments greater

than 130 kNm. The amount of modified data is therefore small.


the rotation of the interface. The procedure to check the rotations is described in section 4.2.2.

The result for the two beams is shown in figure 5.38. The calculated rotations correspond well

to the measured ones, the results are identical.

0 10 20 30 40 50 600

25

50

75

100

125

150

175

200

Deflection [mm]

M [k

Nm

]

inclinometer leftmeasured

0 10 20 30 40 50 600

25

50

75

100

125

150

175

200

Deflection [mm]

M [k

Nm

]

inclinometer rightmeasured



By plotting the displacements under the beams in one diagram (figure 5.39), it can be seen

that the two sides behave similar. The right connection shows a slightly softer tendency with

increasing moment.

0 10 20 30 40 50 600

25

50

75

100

125

150

175

200

Deflection [mm]

M [k

Nm

]

leftright


5.6.3 Evaluation

All the key variables are plotted in figure 5.40.

The two beams seem to show a hysteretic behaviour in the moment-rotation-diagram (different

loading and unloading path). Since nearly no plastic deformations occurred during the test (the

residual deformation under the beams after the test was 2 mm), nearly no energy was dissipated.

The hysteretic behaviour is mainly due to loss in post-tensioning force during the test. Due to

elongation of the tendon the post-tensioning force increases, which also leads to an increase in

oil pressure in the hydraulic system. This leads to an increase of loss in hydraulic fluids, so that

the pressure and therefore the tendon force are deteriorating. The tendon force at the beginning

of the test is 557 kN, at the end 510 kN.

The tendon force (P) increases at a rotation of 6 mrad. The gap reaches the position of the

tendon and therefore elongates it as the load is increased. This elongation leads to an increase

in the tendon force. The force climbs up to 750 kN, where the tests had to be stopped in order

to prevent the tendon from failing.



moment of approximately 50 kNm. The neutral axis depth gets smaller than 300 mm, which

means that the gap reaches the position of the tendon. This observation could also be made

with the tendon force. For the right beam the range of altered data is visible; a discontinuity is

clearly visible at approximately 20 mrad. The left beam also shows a behaviour, which is not

correct. The height x starts to increase from a rotation of 30 mrad, which is not possible. This

5.6. Test 22 49

0 0.01 0.02 0.03 0.04 0.050

50

100

150

200

θ [−]

M [k

Nm

]

leftright

0 0.01 0.02 0.03 0.04 0.050

200

400

600

800

θ [−]

P [k

N]

0 0.01 0.02 0.03 0.04 0.050

100

200

300

400

500

600

θ [−]

x [m

m]

leftrightFSR

0 0.01 0.02 0.03 0.04 0.050

5

10

15

20

25

θ [−]

σ inf [N

/mm

2 ]

leftright


phenomena is due to the error in the LVDTs (out of range).

The stresses exceed 20 MPa, which is not in the expected elastic range any more. The plastic

deformations measured after the test are very small though, each beam had residual deformations

of 2 mm. Large leaps are noticeable for both interfaces. For the left interface it is due some

LVDTs being out of their measuring range, at the right interface it is due to the alteration of

the data, which is very sensitive regarding the stresses.

To have a better overview the same diagrams are plotted in figure 5.41, but only for one load

cycle.


0 0.01 0.02 0.03 0.04 0.050

50

100

150

200

θ [−]

M [k

Nm

]

leftright

0 0.01 0.02 0.03 0.04 0.050

200

400

600

800

θ [−]

P [k

N]

0 0.01 0.02 0.03 0.04 0.050

100

200

300

400

500

600

θ [−]

x [m

m]

leftrightFSR

0 0.01 0.02 0.03 0.04 0.050

5

10

15

20

25

θ [−]

σ inf [N

/mm

2 ]

leftright

Fig. 5.41: Evaluation test 22 one load cycle

Chapter 6

Test summary

The moment-rotation-behaviour of a post-tensioned beam-column timber joint has been anal-

ysed extensively with a series of static bending tests. The timber joint was loaded at the end

of the beams in order to apply a moment to the connection. The tests were conducted with

various forces in the tendon, from 300 kN up to 700 kN. The experimental analysis showed, that

the connection stiffness increases with increasing tendon force.

The tests were conducted with different load cases; a series of test was conducted with an

symmetrical loading, so that the column is only loaded in compression perpendicular to the

grain. An asymmetrical load case was applied in order to load the column in compression and

shear, leading to significantly softer behaviour due to shear deformations in the column.

A final bending test was conducted in order to study the failure mode of the post-tensioned

timber joint. The vertical load on the beams was increased until the tendon elongation got so

high that the test had to be aborted. Therefore, an actual failure did not occur during the test.

However, the estimated strength in the column perpendicular to the grain was exceeded mas-

sively (at least by a factor of two) but only minor damage could be observed after disassembling

the specimen.

The performed tests showed, that a very simple semi-rigid connection can be built with post-

tensioning a timber specimen. Furthermore, the failure mode is not brittle but plastic. The

timber fails due to embedment failure perpendicular to the grain, which only leads to very small

damage in the connection.

52 Chapter 6. Test summary

Appendix A

Drawings

A.1 Specimen and instrumentation

54 Chapter A. Drawings

A.1. Specimen and instrumentation 55

0.04

0.28

0.04

WLV

3

WLO

2

WLV

1

WLV

2

WR

V3

WR

O2

WR

V1

WR

V4

WR

V2

1.25

1.25

0.70.60.7

0.06

1.6

0.36

0.025

0.301

0.437

0.571

0.644

0.622

0.574

0.2990.029

Dur

ch L

Dur

ch R

IL2

IL1

IR1

IR2

1.6

0.06

LVD

T

Incl

inom

eter

Test

spe

cim

en w

ith in

stru

men

tatio

nFr

ont v

iew

1:20

[m]


1.25

1.25

0.70.60.7

WR

V3

WR

O2

WR

V1

WR

V4

WR

V2

0.644

0.571

0.437

0.3010.025

Dur

ch R

Dur

ch L

0.299

0.029

0.574

0.622

IR1

IR2

IL1

IL2

WLV

3

WLO

2

WLV

1

WLV

2

LVD

T

Incl

inom

eter

Test

spe

cim

en w

ith in

stru

men

tatio

nB

ack

view

1:20

[m]


0.7

0.6

0.7

0.1 0.4 0.1

Test Specimen 1:20 [m]

A.2. Specimen and test setup 61

A.2 Specimen and test setup


Test

set

up

1:25

21 1

2


1-1

2-2

Appendix B

Test protocols

68 Chapter B. Test protocols

B.1 Test 13

Tab. B.1: Protocol test 13

Load cycle Load application Notes

No. 0 Tendon to 518 kN FSR connected at 300 kN

No. 1 symmetric 0 → 20 kN


No. 3 symmetric 0 → 60 kN Gap opening at 39 kN


No. 5 right constant to 10 kN, left 0 → 40 kN









No. 14 left constant to 10 kN, right 0 → 40 kN Gap opening at 40 kN


No. 16 left constant to 20 kN, right 0 → 40 kN







B.2. Test 14 69

B.2 Test 14



























B.3 Test 15






No. 3 symmetric 0 → 60 kN (Gap opening at 55 kN)

No. 4 symmetric 0 → 80 kN (Gap opening at 55 kN)


No. 6 left constant to 10 kN, right 0 → 70 kN (Gap opening at 53 kN)





















No. 27 symmetric 0 → 80 kN noise (cracking)

B.4. Test 16 71

B.4 Test 16



























B.5 Test 17































B.6. Test 18 73

B.6 Test 18
































B.7 Test 19

An error occured during the tests. One cylinder was not attached properly. The cylces 1 to 7

are therefore not suitable for analysis.

















B.8. Test 20 75

B.8 Test 20
































B.9 Test 21






























B.10. Test 22 77

B.10 Test 22









No. 6 symmetric 0 → 135 kN WLO1 and WLO2 re-adjusted


No. 8 symmetric 0 → 142 kN Durch L and Durch R re-adjusted






No. 14 symmetric 0 → 151 kN P = 514 kN





No. 19 symmetric 0 → 157 kN P = 510 kN

Appendix C

Test evaluation

80 Chapter C. Test evaluation

C.1 Test 16

C.1.1 Initial compression


−1 −0.5 0 0.50

100

200

300

400

500

600

Displacement [mm]

P [k

N]

WLOWL1WL2WL3

−1 −0.5 0 0.50

100

200

300

400

500

600

Displacement [mm]

P [k

N]

WROWR1WR2WR3WR4

Fig. C.1: Initial compression test 16

The initial compression is the same for both interfaces :

wcomp,left = wcomp,right = 0.23mm (C.1)

C.1.2 Rotation test 16

The procedure to check the rotations is described in section 4.2.2.

0 1 2 3 4 5 6 7 8 9 100

20

40

60

80

100

120


M [k

Nm

]


0 1 2 3 4 5 6 7 8 9 100

20

40

60

80

100

120


M [k

Nm

]


Fig. C.2: Deflection beams test 16

C.1. Test 16 81

C.1.3 Evaluation symmetrical loading

The moment-rotation diagram shows, that the two connections behave similar, again with a

different stiffness for higher moments.


noticed.



moment of approximately 20 kNm.


0 1 2 3 4 5 6 7 8

x 10−3

0

20

40

60

80

100

120

θ [−]

M [k

Nm

]

leftright

0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

700

θ [−]

P [k

N]

leftright

0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

θ [−]

x [m

m]

leftrightFSR

0 1 2 3 4 5 6 7 8

x 10−3

0

2

4

6

8

10

θ [−]

σ inf [N

/mm

2 ]

leftright

Fig. C.3: Evaluation test 16


C.1.4 Evaluation asymmetrical loading

The same observations can be made for both tests, with a constant load on the right beam or

the left beam, respectively.

The rotations calculated from the LVDTs lead to more accurate results than the rotations

calculated from the inclinometers. The moment-rotation-diagram shows a reduction of the

initial stiffness of the connection with decreasing load on the other beam.

The moment of decompression happens basically at the same time compared with the symmetric

loading.

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

Displacement [mm]

M [k

Nm

]

regressionmeasured

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

Displacement [mm]

M [k

Nm

]


Fig. C.4: Deflection beam test 16, constant load on the right beam

0 1 2 3 4 5 6 7 8

x 10−3

0

20

40

60

80

100

120

θ [−]

M [k

Nm

]


0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

θ [−]

x [m

m]


Fig. C.5: Evaluation test 16, constant load on the right beam

C.1. Test 16 83

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

Displacement [mm]

M [k

Nm

]

regressionmeasured

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

Displacement [mm]

M [k

Nm

]


Fig. C.6: Deflection beam test 16, constant load on the left beam

0 1 2 3 4 5 6 7 8

x 10−3

0

20

40

60

80

100

120

θ [−]

M [k

Nm

]


0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

θ [−]

x [m

m]


Fig. C.7: Evaluation test 16, constant load on the left beam


C.2 Test 18

C.2.1 Initial Compression

−1 −0.5 0 0.50

100

200

300

400

500

600

Displacement [mm]

P [k

N]

WLOWL1WL2WL3

−1 −0.5 0 0.50

100

200

300

400

500

600

Displacement [mm]

P [k

N]

WROWR1WR2WR3WR4



wcomp,left = 0.32mm (C.2)


wcomp,right = 0.35mm (C.3)

C.2.2 Rotation

0 1 2 3 4 5 6 7 8 9 100

20

40

60

80

100

120


M [k

Nm

]


0 1 2 3 4 5 6 7 8 9 100

20

40

60

80

100

120


M [k

Nm

]



C.2. Test 18 85


The moment-rotation diagram shows, that the two connections behave similar, again with a

different stiffness for higher moments.


noticed.





0 1 2 3 4 5 6 7 8

x 10−3

0

20

40

60

80

100

120

θ [−]

M [k

Nm

]

leftright

0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

700

θ [−]

P [k

N]

leftright

0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

θ [−]

x [m

m]

leftrightFSR

0 1 2 3 4 5 6 7 8

x 10−3

0

2

4

6

8

10

θ [−]

σ inf [N

/mm

2 ]

leftright






The rotations calculated from the LVDTs lead to more accurate results than the rotations cal-

cualted from the inclinometers. The moment-rotation-diagram show a reduction of the initial

stiffness of the connection with decreasing load on the other beam.

The moment of decompression happens basically at the same rotation compared with the sym-

metric loading.

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

Displacement [mm]

M [k

Nm

]

regressionmeasured

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

Displacement [mm]

M [k

Nm

]



0 1 2 3 4 5 6 7 8

x 10−3

0

20

40

60

80

100

120

θ [−]

M [k

Nm

]


0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

θ [−]

x [m

m]



C.2. Test 18 87

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

Displacement [mm]

M [k

Nm

]

regressionmeasured

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

Displacement [mm]

M [k

Nm

]


Fig. C.13: Deflection beam test 18, constant load on the left beam

0 1 2 3 4 5 6 7 8

x 10−3

0

20

40

60

80

100

120

θ [−]

M [k

Nm

]


0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

θ [−]

x [m

m]




C.3 Test 20

C.3.1 Initial compression

−1 −0.5 0 0.50

100

200

300

400

500

600

Displacement [mm]

P [k

N]

WLOWL1WL2WL3

−1 −0.5 0 0.50

100

200

300

400

500

600

Displacement [mm]

P [k

N]

WROWR1WR2WR3WR4



wcomp,left = 0.29mm (C.4)


wcomp,right = 0.3mm (C.5)

C.3.2 Rotation

0 1 2 3 4 5 6 7 8 9 100

20

40

60

80

100

120


M [k

Nm

]


0 1 2 3 4 5 6 7 8 9 100

20

40

60

80

100

120


M [k

Nm

]



C.3. Test 20 89


The moment-rotation plot shows, that the two connections behave similar, again with a different

stiffness for higher moments.


noticed.




The stresses go up to 9 MPa, which is outside the expected elastic range (no plastic deformations

where observed after the test).

0 1 2 3 4 5 6 7 8

x 10−3

0

20

40

60

80

100

120

θ [−]

M [k

Nm

]

leftright

0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

700

θ [−]

P [k

N]

leftright

0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

θ [−]

x [m

m]

leftrightFSR

0 1 2 3 4 5 6 7 8

x 10−3

0

2

4

6

8

10

θ [−]

σ inf [N

/mm

2 ]

leftright






The rotations calculated from the LVDTs lead to more accurate results than the rotations cal-

culated from the inclinometers. The moment-rotation-diagram shows a reduction of the initial

stiffness of the connection with decreasing load on the right beam.

The moment of decompression happens basically at the same rotation compared with the sym-

metric loading.

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

Displacement [mm]

M [k

Nm

]

regressionmeasured

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

Displacement [mm]

M [k

Nm

]



0 1 2 3 4 5 6 7 8

x 10−3

0

20

40

60

80

100

120

θ [−]

M [k

Nm

]


0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

θ [−]

x [m

m]



C.3. Test 20 91

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

Displacement [mm]

M [k

Nm

]

regressionmeasured

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

Displacement [mm]

M [k

Nm

]


Fig. C.20: Deflection beam test 20, constant load the on left beam

0 1 2 3 4 5 6 7 8

x 10−3

0

20

40

60

80

100

120

θ [−]

M [k

Nm

]


0 1 2 3 4 5 6 7 8

x 10−3

0

100

200

300

400

500

600

θ [−]

x [m

m]



Nomenclature

Abbreviations

DurchL Deflection under the left beam

DurchR Deflection under the right beam

FSR Pressure sensors

IL... Inclination on the left beam

IR... Inclination on the right beam

KMD Load cell

LV DT Linear voltage displacement transducer

WL... Displacement at the left connection

WR... Displacement at the right connection

Upper-case Roman letters

A Cross section area beam

Ap Cross section area tendon

E Modulus of elasticity beam

E0,mean Modulus of elasticity parallel to the grain

E90,mean Modulus of elasticity perpendicular to the grain

Ep Modulus of elasticity tendon

F Applied load on the beam

Gmean Shear modulus

I Moment of inertia beam

Icol Moment of inertia column

Lcant Distance between interface and applied load F

94 Nomenclature

Lp Length tendon

M Moment at the interface

Masymmetric,col Moment in the column due to asymmetrical loading

N Number of strands

P Tendon force

P0 Initial tendon force

PFSR Tendon force when FSR-sensor is mounted

Pmax Applicable design load tendon

W Elastic section modulus beam

Lower-case Roman letters

b Width beam

bs Witdh column

f Distance between two LVDTs

fc,0,k Compressive strength parallel to the grain

fc,90,k Compressive strength perpendicular to the grain

fFSR Factor FSR

fp,k Tensile strength tendon

n Displacement at lower edge of the interface

w′ Inclination beam

wasymmetric Deflection beam due to asymmetric loading

wcalc Calculated deflection beam

wcomp,calc Calculated initial compression

wcomp,left Initial compression left interface

wcomp,right Initial compression right interface

wel,beam Elastic deflection beam

wmeasured Measured deflection beam

x Height compressive zone

xincl Position inclinometer measured from interface

y Displacement measured with LVDT

Nomenclature 95

Greek letters

σinf Stresses interface

θ Rotation

θasymmetric Rotation asymmetric load case

96 Nomenclature

Bibliography

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